Behavioral, neuropsychological, and brain imaging research points to a dedicated system for processing number that is shared across development and across species (Dehaene, 1998; Feigenson et al., 2004). This foundational Approximate Number System (henceforth, the ANS) forms amodal representations of the number of objects, sounds, or events in a scene. Importantly, it is imprecise, and in this way differs from exact verbal counting. This system serves as a basis for more sophisticated, uniquely human mathematical abilities involving symbolic calculation. While these aspects of this system for numerical approximation have been well documented, they also raise important questions. First, how does the acuity of the approximate number system change over the course of development? Evidence suggests that infants have less precise ANS representations than adults, yet qualitative changes in the ANS between infancy and adulthood remain almost entirely undescribed. Second, how early in development is the ANS engaged, and what is its early acuity? At present nothing is known of numerical approximation in children younger than 6 months old. Third, what are the individual differences in the acuity of this system across the lifespan? Although previous research suggests that, on average, adults can discriminate arrays differing by a 7:8 ratio, individual adults may vary widely in ANS acuity. Fourth, what are the individual differences in children's numerical approximation abilities? Variation in the precision of individual children's ANS representations may remain stable over development, or may fluctuate with age and experience. Fifth, what is the relationship between individual differences in the acuity of the ANS and performance on tests of symbolic math ability? Identifying the relationship between the ANS and math performance may be critical to the goals of identifying subtypes of math deficits and improving children's math proficiency. Sixth, what mechanism underlies developmental improvement in the ANS? While maturation may play a role, experience may also serve to hone ANS acuity. The current project aims to answer these questions by examining the numerical abilities of infants, children, and adults, and in doing so to characterize the development of a foundational mechanism for representing number. Ultimately, the proposed studies will contribute to the broader goal of understanding continuities and discontinuities in the development of quantitative knowledge. Given that by some estimates 3 to 7% of the general population (1 in 15) suffers from some form of numerical processing deficit (dyscalculia), this project may have important repercussions for studying impairments in numerical cognition. Patients suffering damage to the ANS due to disease or stroke, those with genetically mediated dyscalculia, and children with math- specific deficits will benefit from an understanding of the development and function of the Approximate Number System because of the importance of numerical reasoning to daily and professional life. PUBLIC HEALTH RELEVANCE: The proposed project aims to contribute to the larger goal of understanding numerical thinking by investigating approximate number representations in normally-developing infants, children, and adults. In documenting the development of numerical approximation, individual differences in numerical approximation, and the relationship between numerical approximation and mathematics performance, this project may have repercussions for understanding disorders of numerical processing and for strategies for improving math education.